Weird deviation when extruding vertexes
Try this - don't snap to anything.  Get into Ortho view mode so you're looking flat at the side to be extruded, extrude one vertice only a small distance in the axis that will take it along top edge.  Then press G and move your mouse down so the loose vertice is near but not touching the bottom right vertice.  

Highlite the loose vertice, and with shift held, highlite the 2nd vertice at the corner, press ALT-M and select "first to Last" or similar, to "marry them". (my term)

If that doesn't deform the cube's shape, do the same with the other side.  Round it all off by removing any doubles.